Many parts are comprised of composite materials, so it is important to inspect the composite material to find any flaws within the material. The traditional technique of inspecting composite material is to take an ultrasonic transducer, put the transducer over the part and immerse the part in fluid so that there is a means of transmitting the energy from the transducer into the part. To determine if there is a flaw, a wave is propagated through the fluid so that it hits the back surface and reflects back, traveling with the velocity of sound in the material, typically 6000 m/s. Based on this information, it can be determined how much time it will take the wave to travel between the front and back surface. With this information, the gap between the two surfaces can be determined. Once the gap is known, a threshold is set and when signals are detected greater than this threshold, a flaw is present as the signal is reflecting off the flaw and not the back surface. If there is no flaw present in the part, a clean back surface reflection will be seen on an oscilloscope.
The method described above is utilized to inspect various parts made out of composite materials such as the wing of an aircraft. Every spot on the part, in this case an aircraft wing, must be inspected so the transducer scans the part in a serpentine manner. To do this, the transducer is put on a X-Y movable motion controller. Setting the threshold is very important because depending on the size of the threshold, flaws in the composite material can be ignored as small and not causing a problem or included as the flaw will cause a problem. Composite materials are inspected this way as long as the propagating wave is perpendicular to the laminating plies of the composite material regardless of whether the composite is isotropic or anisotropic. Curved composites cannot be inspected this way.
The method described above is a synthetic aperture focusing technique (SAFT) and was originally developed in order to improve the signal to noise ratio and lateral resolution capability in radar applications. Later, this approach was found useful for the same reasons in ultrasonic signal processing. The typical SAFT technique for nondestructive evaluation uses a focused transducer that is scanned over the surface of a part with a series of A-scans (data presentations) recorded in a pulse-echo manner. These A-scans can then be time shifted and summed at each A-scan position at a chosen focal depth to yield enhanced A-scans of the depth. This enhancement is due to constructive interference at a defect and destructive interference of any noise. Although SAFT was originally developed for isotropic materials, it has recently been extended to anisotropic materials; however, it has been limited to unidirectional or homogenized composites.
SAFT in Single Layer Media
The synthetic aperture focus (SAFT) is achieved by time shifting and summing the A-scans surrounding the point of possible defect. A depth is chosen to focus at and the time shifts are computed for the A-scan data at surrounding coordinates. The time shift is computed by taking twice the total distance from the probe coordinates to the focal coordinates divided by the group velocity, v, for the energy-flux direction. The shortest travel time will be when the probe is directly above the focal point, at depth z below, this travel time is given by.
                              T          0                =                              2            ⁢            z                    v                                    (        1        )            As the probe coordinates move in the x-y plane and are no longer directly over the focal point the travel time is given by
                    T        =                              2            ⁢                                                            x                  2                                +                                  y                  2                                +                                  z                  2                                                              v                                    (        2        )            The time shift that has to be made to the A-scan at any coordinate is then justΔT=T−T0  (3)A new A-scan is then saved at that focal point by the summation of all the time shifted A-scans, this summation is given by equation 4 where A is the new A-scan, n is the number of summed waveforms, Ai is the A-scan being summed that is time shifted by ΔT.
                    A        =                              n                          -              1                                ⁢                                    ∑                              i                =                1                            n                        ⁢                                          A                i                            ⁡                              (                                  Δ                  ⁢                                                                          ⁢                  T                                )                                                                        (        4        )            This summation is done at all coordinates that A-scans were recorded for any depth that needs to be focused at. Unlike using lenses to focus at a depth in a material, by using the SAFT algorithm, only one scan of the part is needed and the focusing at any chosen depth is done by the algorithm. FIGS. 1 and 2 illustrate the variation in time shifts that are expected in isotropic vs. anisotropic media. FIG. 1 illustrates a time shift for aluminum with a focus depth of 20 in arbitrary units. FIG. 2 is the time shift for a unidirectional graphite-epoxy with fibers oriented with the y-axis focused at a depth of 20 in arbitrary units.
Utilizing SAFT in multilayer media is an extension of SAFT for a single layer. First, it is assumed that there is a perfectly bonded interface between each of the layers in the media. At each layer Snell's law is calculated using the wavenormal and phase velocity of each layer. Starting in the first layer a guess is made that a wavenormal will go directly to the desired focal coordinates in a straight line path and as a result the phase velocity is computed. The desired focal coordinates are determined by guessing where a flaw is in the material. Then using Snell's law, the Christoffel equation, and the global stiffness matrix of each layer, the wavenormal and phase velocity in each layer of the media can be computed. By knowing the wavenormal and phase velocities in every layer, the energy-flux direction and group velocity in each layer can be computed. All of the energy-flux directions are then summed and a determination is made as to if the propagating wave goes to the desired focal coordinates. If the media were isotropic, the correct focal coordinates would be immediately determined without any guess work as group and velocity are the same and there would be no beam skew or refraction due to Snell's law. In an anisotropic media, however, the path would have to be going in a symmetry direction in every layer and the wave velocity would have to stay the same in every layer for the correct focal coordinates to be determined the first time. This is only the situation if the wave is at normal incidence at each layer (i.e. directly above the focal coordinates); therefore the wave is perpendicular to the plane in which the fibers are running in each layer. What is needed is an algorithm utilizing SAFT that can inspect materials with multiple anisotropic layers as commonly used in composite fabrication.